Method and apparatus for video coding

ABSTRACT

A method of processing point cloud data at a decoder can include receiving three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point. Each of the first points can be associated with a reconstructed attribute value. A group of neighboring points of the current point can be determined from the first points. A first index is received and the first index indicates a reconstructed attribute value selected from the reconstructed attribute values of the plurality of neighboring points. The reconstructed attributed value indicated by the first index is determined based on a rate-distortion decision function. An attribute distance for each of the neighboring points can be determined based on the reconstructed attribute values of the neighboring points.

INCORPORATION BY REFERENCE

This present disclosure claims the benefit of priority to a series of U.S. Provisional Application No. 62/740,312, filed on Oct. 2, 2018, and 62/740,917, filed on Oct. 3, 2018, which are incorporated by reference herein in their entirety.

TECHNICAL FIELD

The present disclosure describes embodiments generally related to video coding.

BACKGROUND

The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.

Three-dimensional (3D) representations of the world are enabling more immersive forms of interaction and communication, and also allow machines to understand, interpret, and navigate the world. Point clouds have emerged as one of such 3D enabling representations. The Moving Picture Experts Group (MPEG) has identified a number of use cases associated with point cloud data, and developed corresponding requirements for point cloud representation and compression.

SUMMARY

Aspects of the disclosure provide methods and apparatuses for processing point cloud data. In an embodiment, a method of processing point cloud data at a decoder is provided. In the method, 3D coordinates of a set of points of a point cloud including first points and a current point are received. Each of the first points is associated with a reconstructed attribute value. A group of neighboring points of the current point is determined from the first points. An index is associated with each of the reconstructed attribute values of the determined neighboring points. The reconstructed attributed value indicated by the index is determined based on a rate-distortion decision function. An index of a reconstructed attribute value selected from the reconstructed attribute values of the determined neighboring points is received. The reconstructed attribute value having the received index is determined to be an attribute prediction of the current point.

In another embodiment, a method of processing point cloud data at a decoder is provided. In the method, three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point are received. Each of the first points is associated with a reconstructed attribute value. A group of neighboring points of the current point is determined from the first points based on a geometric distance between each of the first points and the current point. An index is associated with the reconstructed attribute value of each of the plurality of neighboring points. A most probable index list of a predetermined size for the current point is generated based on a most probable index of a geometrically closest neighboring point of the plurality of neighboring points. A most probable index for the current point from the most probable index list is received. The reconstructed attribute value associated with the received most probable index for the current point is a best predication candidate among the reconstructed attribute values of the plurality of neighboring points.

Further, an apparatus of processing point cloud data can be provided. The apparatus includes process circuitry that can be configured to receive 3D coordinates of a set of points of a point cloud including first points and a current point. Each of the first points is associated with a reconstructed attribute value. The processing circuitry is configured to determine a group of neighboring points of the current point from the first points. An index is associated with each of the reconstructed attribute values of the determined neighboring points. The processing circuitry is further configured to determine the reconstructed attributed value indicated by the index based on a rate-distortion decision function. An index of a reconstructed attribute value selected from the reconstructed attribute values of the determined neighboring points is received. The processing circuitry is further configured to determine the reconstructed attribute value having the received index to be an attribute prediction of the current point.

In another embodiment, an apparatus of processing point cloud data is provided. The apparatus includes process circuitry that can be configured to receive three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point. Each of the first points is associated with a reconstructed attribute value. The processing circuitry is configured to determine a group of neighboring points of the current point from the first points based on a geometric distance between each of the first points and the current point. An index is associated with the reconstructed attribute value of each of the plurality of neighboring points. The processing circuitry is configured to generate a most probable index list of a predetermined size for the current point based on a most probable index of a geometrically closest neighboring point of the plurality of neighboring points. The processing circuitry is further configured to receive a most probable index for the current point from the most probable index list. The reconstructed attribute value associated with the received most probable index for the current point is a best predication candidate among the reconstructed attribute values of the plurality of neighboring points.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosed subject matter will be more apparent from the following detailed description and the accompanying drawings in which:

FIG. 1 shows a recursive subdivision process in accordance with an embodiment.

FIG. 2 shows a level of detail (LOD) generation process in accordance with an embodiment.

FIG. 3 shows an exemplary encoder in accordance with an embodiment.

FIG. 4 shows an exemplary decoder in accordance with an embodiment.

FIG. 5 shows an example of associating indices with a group of candidate neighboring samples of a current point in accordance with an embodiment.

FIG. 6 shows an example of encoding indices using truncated unary code.

FIG. 7 shows an example of generating a most probable index list for a sample according to an embodiment of the disclosure.

FIG. 8 shows an example of associating indices with multiple groups of candidate neighboring samples in accordance with an embodiment.

FIG. 9 shows an example of assigning indices based on costs of attribute vectors in accordance with an embodiment.

FIG. 10 shows an example of indexing sorted samples by additionally considering a geometric distance of a candidate predictor sample from a current sample in accordance with an embodiment.

FIG. 11 shows an example of a gradual transition of the number of neighbors for Winner-Take-All (WTA) prediction according to an embodiment of the disclosure.

FIG. 12 shows an attribute prediction process according to an embodiment of the disclosure.

FIG. 13 shows an attribute prediction process according to another embodiment of the disclosure.

FIG. 14 is a schematic illustration of a computer system in accordance with an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

I. Point Cloud Compression Systems

1. Point Cloud Data

Point cloud data is used to represent a three-dimensional (3D) scene or object in some emerging applications such as immersive virtual reality (VR)/augmented reality (AR)/mixed reality (MR), automotive/robotic navigation, medical imaging, and the like. A point cloud includes a collection of individual 3D points. Each point is associated with a set of 3D coordinates indicating a 3D position of the respective point and a number of other attributes such as color, surface normal, opaque, reflectance, etc. In various embodiments, input point cloud data can be quantized and subsequently organized into a 3D grid of cubic voxels that can be described using an octree data structure. A resulting voxelized octree facilitates the traversal, search, and access of the quantized point cloud data.

A point cloud is a set of points in a 3D space, each with associated attributes, e.g., color, material properties, etc. Point clouds can be used to reconstruct an object or a scene as a composition of such points. They can be captured using multiple cameras and depth sensors in various setups, and may be made up of thousands and even billions of points in order to realistically represent reconstructed scenes.

Compression technologies are needed to reduce the amount of data required to represent a point cloud. As such, technologies are needed for lossy compression of point clouds for use in real-time communications and six Degrees of Freedom (6 DoF) virtual reality. In addition, technologies are sought for lossless point cloud compression in the context of dynamic mapping for autonomous driving and cultural heritage applications, etc. Further, standards are needed to address compression of geometry and attributes (e.g., colors and reflectance), scalable/progressive coding, coding of sequences of point clouds captured over time, and random access to subsets of the point cloud.

2. Coordinates Quantization

In an embodiment, coordinates of points in the input cloud data can first be quantized. For example, real number values of the coordinates may be quantized into integer values. After the quantization, more than one point may share a same position in some voxels. Those duplicate points optionally can be merged into a single point.

3. Geometry Coding Based on an Octree

FIG. 1 shows a recursive subdivision process (100) in accordance with an embodiment. The process (100) can be performed to generate an octree structure to represent positions of a set of points in a point cloud. As shown, a cubical axis-aligned bounding box (101) containing the set of points is first defined. Then, the bounding box (101) is recursively subdivided to build the octree structure. As shown in FIG. 1, at each stage, a current cube can be subdivided into 8 sub-cubes. An 8-bit code, referred to as an occupancy code, can be generated to indicate whether each of the 8 sub-cubes contains points. For example, each sub-cube is associated with a 1-bit value. If the sub-cube is occupied, the respective sub-cube has a bit value of 1; otherwise, the respective sub-cube has a bit value of 0. Occupied sub-cubes can be divided until a predefined minimum size of the sub-cubes is reached. A sub-cube of the minimum size is a voxel corresponding to the octree structure. A sequence of occupancy codes can thus be generated, and subsequently be compressed and transmitted from an encoder to a decoder. By decoding the occupancy codes (e.g., performing an octree decoding process), the decoder can obtain a same octree structure as the encoder, or an estimation of the octree structure.

3. Attribute Transfer

As a result of the octree generation or coding process, at the encoder side, a sub-cube with the minimum size may contain more than one point. Thus, a position corresponding to a voxel (e.g., a center of the respective sub-cube) may correspond to multiple sets of attributes from multiple points. In such a scenario, in an embodiment, an attribute transfer process can be performed to determine one set of attributes based on the multiple sets of attributes for the respective voxel. For example, an averaged attribute of a subset of nearest neighboring points can be used as an attribute of the respective voxel. Different methods may be employed in various embodiments for attribute transfer purposes.

4. Level of Detail (LOD) Generation

FIG. 2 shows a level of detail (LOD) generation process (200) in accordance with an embodiment. The process (200) can be performed on the quantized positions (e.g., voxel positions) ordered according to the octree decoding process. As a result of the process (200), the points can be re-organized or re-ordered into a set of refinement levels. The process (200) can be performed identically at the encoder and decoder. A subsequent attribute coding process can be performed at the encoder or decoder according to the order defined by the process (200) (referred to as the LOD-based order).

Specifically, FIG. 2 shows three LODs: LOD0, LOD1, and LOD2. A Euclidean distance, d0, d1, or d2, can be specified for LOD0, LOD1, and LOD2, respectively. A subset of points P0-P9 is included in each LOD. The distances between each pair of points in the respective LOD is larger than or equal to the respective Euclidean distance. The Euclidean distances can be arranged in a manner that d0>d1>d2. Under such arrangement, a higher refinement level includes fewer points that are farther from each other, and provides a coarser representation of the point cloud, while a lower refinement level includes more points closer to each other, and provides a finer representation of the point cloud.

As a result of the above LOD generation process (200), the points in an original order (octree decoding order) from P0 to P9 can be re-organized into an LOD-based order: P0, P5, P4, P2, P1, P6, P3, P9, P8, and P7.

5. Attributes Prediction

The attributes associated with the point cloud can be encoded and decoded in the order defined by the LOD generation process. For example, point by point, in the LOD-based order, an attribute prediction of each current point (a point currently under processing) can be determined by performing an attribute prediction process at the encoder and/or decoder. A similar attribute prediction process can be performed at the encoder and the decoder. At each step, only the already encoded/decoded points are considered for prediction. More specifically, the attribute values (a₁)_(i∈0 . . . k−1) are predicted by using a linear interpolation process based on the distances of the nearest neighbors of point i.

_(i) represents the set of the k-nearest neighbors of the current point i and

represents their decoded/reconstructed attribute values and

their distances to the current point. The predicted attribute value â_(i) is then given by:

${\hat{a}}_{i} = {{Round}\mspace{11mu} \left( {\frac{1}{k}{\sum_{j \in _{i}}{\frac{\frac{1}{\delta_{j}^{2}}}{\sum_{j \in _{i}}\frac{1}{\delta_{j}^{2}}}{\overset{\sim}{a}}_{j}}}} \right)}$

The geometric locations of all the point clouds are already available when attributes are coded. In addition, the neighboring points together with their reconstructed attribute values are available both at the encoder and the decoder as a KD-Tree structure is used to facilitate the nearest-neighbor search for each point in an identical manner.

With the obtained attribute prediction, at the encoder, a residual signal can be generated by subtracting the attribute prediction value from a respective original attribute value of the current point. The residual signal can then, individually or in combination with other residual signals, be further compressed. For example, transform and/or quantization operations may be performed, and followed by entropy coding of resulting signals. The compressed residual signal can be transmitted to the encoder in a bit stream.

At the decoder, a residual signal can be recovered by performing an inverse of the coding process at the encoder for coding a residual signal. With the obtained attribute prediction and the recovered residual signal corresponding to the current point, a reconstructed attribute of the current point can be obtained. In a similar way, this reconstruction operation may take place at the encoder to obtain a reconstructed attribute.

Various attribute prediction techniques can be employed in various embodiments to determine the attribute prediction. Typically, the attribute prediction of the current point is performed using previously reconstructed attributes of points neighboring the current point. When the attribute prediction process is started, based on the LOD-based order, reconstructed attribute values of points prior to the current point are already available. In addition, from the octree coding or decoding process, positions (3D coordinates) of the points in the point cloud are also available. Accordingly, the attribute prediction process can be performed with the knowledge of the reconstructed attributes and 3D coordinates of the neighboring points of the current point.

In some embodiments, a set of neighboring points of the current point can first be determined using various algorithms. In one example, a k-d tree structure based searching process can be performed to determine a set of points nearest to the current point.

In some embodiments, a geometric distance and/or attribute distance based approach is used to determine the attribute prediction. The prediction attribute can be determined based on a weighted sum (or weighted average) of reconstructed attributes of a set of determined neighboring points at the encoder or decoder. For example, with the set of determined neighboring points, the weighted sum (or weighted average) of the reconstructed attributes of the determined neighboring points can be determined to be the prediction attribute at the encoder or decoder. For example, a weight used in the weighted sum based technique (also referred to as an interpolation based technique) can be an inverse of (or inversely proportional to) a geometric distance, or an attribute distance. Alternatively, the weight can be a bilateral weight derived from a combination of a geometric distance based weight (a geometric eight) and an attribute distance based weight (an attribute weight).

In some embodiments, a rate-distortion (RD) based approach is used to determine the attribute prediction. For example, a candidate index may be associated with each reconstructed attribute value of the set of neighboring points at the encoder or decoder. At the encoder, an RD optimization based process can be performed to evaluate which one of the candidate reconstructed attribute values of the neighboring points is the best choice to be used as the attribute prediction. For example, a distortion can be measured by a difference between the original (or true) attribute value of the current point and a candidate prediction (candidate reconstructed attribute value). A rate can be a cost of encoding the index of the selected candidate prediction. A Lagrangian RD cost function can be defined to determine the best prediction signal candidate. A candidate index of the selected candidate prediction can thus be signaled to the decoder.

Accordingly, the decoder may first determine a same set of neighboring points of a respective current point, and associate indices to the reconstructed attribute values of the same set of neighboring points in a similar way as the encoder side. Then, the decoder can determine an attribute prediction from the reconstructed attribute values of the neighboring points using the signaled candidate index.

6. Coding System Examples of Point Cloud Compression

FIG. 3 shows an exemplary encoder (300) in accordance with an embodiment. The encoder can be configured to receive point cloud data and compress the point cloud data to generate a bit stream carrying compressed point cloud data. In an embodiment, the encoder (300) can include a position quantization module (310), a duplicated points removal module (312), an octree encoding module (330), an attribute transfer module (320), an LOD generation module (340), an attribute prediction module (350), a residual quantization module (360), an arithmetic coding module (370), an inverse residual quantization module (380), an addition module (381), and a memory (390) to store reconstructed attribute values.

As shown, an input point cloud (301) can be received at the encoder (300). Positions (3D coordinates) of the point cloud (301) are provided to the quantization module (310). The quantization module (310) is configured to quantize the coordinates to generate quantized positions. The optional duplicated points removal module (312) is configured to receive the quantized positions and perform a filter process to identify and remove duplicated points. The octree encoding module (330) is configured to receive filtered positions from the duplicated points removal module, and perform an octree-based encoding process to generate a sequence of occupancy codes that describe a 3D grid of voxels. The occupancy codes are provided to the arithmetic coding module (370).

The attribute transfer module (320) is configured to receive attributes of the input point cloud, and perform an attribute transfer process to determine an attribute value for each voxel when multiple attribute values are associated with the respective voxel. The attribute transfer process can be performed on the re-ordered points output from the octree encoding module (330). The attributes after the transfer operations are provided to the attribute prediction module (350). The LOD generation module (340) is configured to operate on the re-ordered points output from the octree encoding module (330), and re-organize the points into different LODs. LOD information is supplied to the attribute prediction module (350).

The attribute prediction module (350) processes the points according to an LOD-based order indicated by the LOD information from the LOD generation module (340). The attribute prediction module (350) generates an attribute prediction for a current point based on reconstructed attributes of a set of neighboring points of the current point stored in the memory (390). Prediction residuals can subsequently be obtained based on original attribute values received from the attribute transfer module (320) and locally generated attribute predictions. When candidate indices are used in the respective attribute prediction process, an index corresponding to a selected prediction candidate may be provided to the arithmetic coding module (370).

The residual quantization module (360) is configured to receive the prediction residuals from the attribute prediction module (350), and perform quantization to generate quantized residuals. The quantized residuals are provided to the arithmetic coding module (370).

The inverse residual quantization module (380) is configured to receive the quantized residuals from the residual quantization module (360), and generate reconstructed prediction residuals by performing an inverse of the quantization operations performed at the residual quantization module (360). The addition module (381) is configured to receive the reconstructed prediction residuals from the inverse residual quantization module (380), and the respective attribute predictions from the attribute prediction module (350). By combining the reconstructed prediction residuals and the attribute predictions, the reconstructed attribute values are generated and stored to the memory (390).

The arithmetic coding module (370) is configured to receive the occupancy codes, the candidate indices (if used), the quantized residuals (if generated), and other information, and perform entropy encoding to further compress the received values or information. As a result, a compressed bitstream (302) carrying the compressed information can be generated. The bitstream (302) may be transmitted, or otherwise provided, to a decoder that decodes the compressed bitstream, or may be stored in a storage device.

FIG. 4 shows an exemplary decoder (400) in accordance with an embodiment. The decoder (400) can be configured to receive a compressed bitstream and perform point cloud data decompression to decompress the bitstream to generate decoded point cloud data. In an embodiment, the decoder (400) can include an arithmetic decoding module (410), an inverse residual quantization module (420), an octree decoding module (430), an LOD generation module (440), an attribute prediction module (450), and a memory (460) to store reconstructed attribute values.

As shown, a compressed bitstream (401) can be received at the arithmetic decoding module (410). The arithmetic decoding module (410) is configured to decode the compressed bitstream (401) to obtain quantized residuals (if generated) and occupancy codes of a point cloud. The octree decoding module (430) is configured to determine reconstructed positions of points in the point cloud according to the occupancy codes. The LOD generation module (440) is configured to re-organize the points into different LODs based on the reconstructed positions, and determine an LOD-based order. The inverse residual quantization module (420) is configured to generate reconstructed residuals based on the quantized residuals received from the arithmetic decoding module (410).

The attribute prediction module (450) is configured to perform an attribute prediction process to determine attribute predictions for the points according to the LOD-based order. For example, an attribute prediction of a current point can be determined based on reconstructed attribute values of neighboring points of the current point stored in the memory (460). The attribute prediction module (450) can combine the attribute prediction with a respective reconstructed residual to generate a reconstructed attribute for the current point.

A sequence of reconstructed attributes generated from the attribute prediction module (450) together with the reconstructed positions generated from the octree decoding module (430) corresponds to a decoded point cloud (402) that is output from the decoder (400) in one example. In addition, the reconstructed attributes are also stored into the memory (460) and can be subsequently used for deriving attribute predictions for subsequent points.

In various embodiments, the encoder (300) and decoder (400) can be implemented with hardware, software, or combination thereof. For example, the encoder (300) and decoder (400) can be implemented with processing circuitry such as one or more integrated circuits (ICs) that operate with or without software, such as an application specific integrated circuit (ASIC), field programmable gate array (FPGA), and the like. For another example, the encoder (300) and decoder (400) can be implemented as software or firmware including instructions stored in a non-volatile (or non-transitory) computer-readable storage medium. The instructions, when executed by processing circuitry, such as one or more processors, causing the processing circuitry to perform functions of the encoder (300) and decoder (400).

It is noted that the attribute prediction modules (350) or (450) configured to implement the attribute prediction techniques disclosed herein can be included in other decoders or encoders that may have similar or different structures from what is shown in FIG. 3 and FIG. 4. In addition, the encoder (300) and decoder (400) can be included in a same device, or separate devices in various examples.

II. Attribute Prediction Techniques

A geometric distance based interpolation technique can be used to determine an attribute prediction of a current point. For example, when performing an attribute prediction for the current point, 3D coordinates of points in a point cloud may already be available from an octree coding or decoding process. An LOD-based order of the points is also known from an LOD generation process. Reconstructed attribute values of the points prior to the current point according to the LOD-based order are also available.

With the knowledge of the 3D coordinates and the LOD-based order, a set of nearest neighboring points of the current point can be determined from the points processed prior to the current point. Then, a set of geometric weights of the neighboring points can be determined. A geometric weight of a neighboring point can be defined to be an inverse of (or inversely proportional to) a geometric distance between the neighboring point and the current point. Subsequently, the attribute prediction of the current point can be determined based on the set of geometric weights and the reconstructed attribute values. For example, a weighted average of the reconstructed attribute values of the neighboring points can be determined to be the attribute prediction of the current point. The weighted average can be a weighted sum of the reconstructed attribute values of the neighboring points divided by a sum of the set of geometric weights.

In the above geometric distance based interpolation technique, the weighting factor, which can be the inverse of the geometric distance between the current point and each of the neighboring points, can be used to form a weighted sum of neighboring attribute values as an attribute prediction. According to an aspect of the disclosure, in areas of the point cloud where the attribute values are smoothly varying or homogeneous, the above geometry based technique tends to be effective. However, in other cases, there can be very low correlation between the attribute distance and the geometric distance, thereby rendering the geometry-based weighted prediction of attribute less effective. Accordingly, other attribute prediction techniques are described in this disclosure that can be employed to form prediction signals for point-cloud attributes taking into account the characteristics of respective attribute signals. Compared with the geometry based techniques, more accurate attribute prediction with higher coding efficiency can be achieved when attribute characteristics are considered for the attribute prediction.

1. Attribute Distance and Bilateral Distance

As an alternative to or in combination with the geometric distance (GEOD), an attribute distance can be defined and used as a measure of proximity of neighboring points used in prediction for attribute coding.

In one embodiment, a median of reconstructed attribute values of neighboring points is adopted to derive the attribute-distance. Then, a deviation of the reconstructed attribute of each neighboring point from the median is defined as a median-attribute distance (MDAD). This median-attribute distance can be calculated at an encoder as well as a decoder since reconstructed attribute values used for calculating the median-attribute distance are available at both the encoder and the decoder.

In one embodiment, a mean of the reconstructed attribute values of neighboring points is adopted to derive the attribute-distance. Then, the deviation of the reconstructed attribute of each neighboring point from the mean is defined as the mean-attribute distance (MNAD). This mean-attribute distance can be calculated at the encoder or decoder since the mean-attribute distance is based on the reconstructed attribute values available at both the encoder and decoder.

In one embodiment, either the median-attribute or the mean-attribute distance can be used as a sole measure of proximity thereby giving a definition of an attribute-based weight (W_(a)) used for attribute prediction as follows:

${{\left. W_{a} \right.\sim\frac{1}{MDAD}}\mspace{14mu} {or}\mspace{14mu} {\left. W_{a} \right.\sim\frac{1}{MNAD}}},$

where “˜” represents the respective weight is equal or proportional to the inverse of the respective attribute distance.

In another embodiment, either MDAD or MNAD as defined above can be used in combination with the geometric distance (GEOD) to form a bilateral distance as a measure of proximity thereby giving a definition of a bilateral weight (Wb) used for attribute prediction as follows:

${\left. W_{b} \right.\sim\frac{1}{MDAD}}W_{g}\mspace{14mu} {or}\mspace{14mu} {\left. W_{b} \right.\sim\frac{1}{MNAD}}W_{g}$

where W_(g) represents a geometric weight and is defined as follows:

${\left. W_{g} \right.\sim\frac{1}{GEOD}}.$

Further, in some embodiments, a combination of MDAD, MNAD, and GEOD can be used.

2. Winner-Take-All (WTA) Prediction with Various Distance Metrics

In some embodiments, a winner-takes-all (WTA) approach used to form an attribute prediction of a current point based on available reconstructed neighboring samples (e.g., reconstructed attribute values of neighboring points of the current point) based on geometric, attribute, and/or bilateral measures such W_(g), W_(a) and W_(b). For example, a reconstructed neighboring attribute value with a highest weight among the reconstructed neighboring attribute values can be determined to be the attribute prediction of the current point. In mathematical form, the WTA approach can be represented as:

PRED_(WTA) =P _(m),

where PRED_(WTA) represents the attribute prediction,

${m = {\underset{i}{argmax}\; {W_{g}\left( P_{i} \right)}}},{m = {{\underset{i}{argmax}\; {W_{a}\left( P_{i} \right)}\mspace{14mu} {or}\mspace{14mu} m} = {\underset{i}{argmax}\; {W_{b}\left( P_{i} \right)}}}},$

and Pi is the i-th reconstructed neighboring attribute value available for prediction.

In one embodiment, the WTA approach is always used when forming or choosing a prediction signal. In another embodiment, the encoder can signal for a sample or a group of samples including but not limited to macro-blocks, a frame/slice/tile, or the entire sequence whether the WTA approach is used or not. A sample can refer to one or more attribute values associated with a point in a point cloud.

The WTA approach can also be used only when a condition specifying variability or the homogeneity of attribute values in the neighbor of the current point are satisfied. One example of the measurement of variability is a maximum difference of neighboring attribute values. For example, when the variability of the reconstructed neighboring attribute values of the current point is greater or equal to a threshold, the WTA approach can be used.

Further, the WTA approach can be used only when the quantization parameter (QP) meets a certain threshold condition (e.g., smaller than a threshold, which may indicate a high variability of the reconstructed neighboring attribute values of the current point). Otherwise, other types of attribute prediction such as weighted prediction (e.g., geometric, attribute, or bilateral weight based prediction) can be used. In addition, coding conditions leading to similar effects of quantization can also be used separately or in combination with QP to determine which attribute prediction approach is to be used.

3. Weighted Average Prediction with Various Distance Metrics

In some embodiments, a weighted sum of reconstructed neighboring attribute values is used to form an attribute prediction based on measures such as W_(g), W_(a) and/or W_(b). For example, a weighted-sum based attribute prediction can be derived according to:

${{PRED}_{WTS} = \frac{\sum\limits_{i = 1}^{N}{{W_{a}\left( P_{i} \right)}P_{i}}}{\sum\limits_{i = 1}^{N}{W_{a}\left( P_{i} \right)}}},{or}$ ${{PRED}_{WTS} = \frac{\sum\limits_{i = 1}^{N}{{W_{b}\left( P_{i} \right)}P_{i}}}{\sum\limits_{i = 1}^{N}{W_{b}\left( P_{i} \right)}}},$

where PRED_(WTS) represents a weighted-sum (or weighted-average) based attribute prediction, N is a number of reconstructed neighboring attribute values, and P_(i) is the i-th reconstructed neighboring attribute value available for prediction.

In an embodiment, the weighted average or weighted sum is used to form an attribute prediction only when the quantization parameter QP meets a certain threshold condition (e.g., larger than a threshold). Otherwise, other approaches such as WTA based prediction can be used in some embodiments. Coding conditions leading to similar effects of quantization can also be used separately or in combination with QP to determine which attribute prediction approach is to be used.

4. Median or Weighted Median Prediction with Various Distance Metrics

In some embodiments, a median or weighted median of reconstructed neighboring attribute values are used to form an attribute prediction of a current point. In an embodiment, a median of the reconstructed neighboring attribute values is used as the attribute prediction.

In an embodiment, a weighted median of the reconstructed neighboring attribute values is used as the attribute prediction based on weights determined by measures such as W_(a) and/or W_(b). For example, a cost-function ƒ(X_(j)) can be defined for each neighboring attribute-vector X_(j) as follows

ƒ(X _(j))

W _(j)Σ_(i=1) ^(N) ∥X _(j) −X _(i)∥_(p)

where X_(i) is a neighboring attribute-vector with i=1, . . . , N, j=1, . . . , N, N is the number of neighboring points corresponding to the reconstructed neighboring attribute values, and ∥∩∥_(p) is the X_(p) norm, for which p=1 or p=2 can be chosen. A weight W_(j) can represent the relative importance of the candidate vector X_(j) and the smaller W_(j) is, the more important X_(j) is. The vector X_(j) minimizing ƒ(X_(j)) above is defined as the weighted vector median (X_(VM)). For example, when each neighbor attribute-vector X_(j) is one dimensional and represents a reconstructed neighboring attribute value, a weighted median attribute value can be calculated based on the cost-function ƒ(X_(j)). For example, an inverse of W_(a) or W_(b) can be used as the W_(j).

In an embodiment, the median or a weighted median is used as an attribute prediction only when the quantization parameter QP meets a certain threshold condition (e.g., smaller or equal to a threshold). Otherwise, other approaches such as the weighted-sum prediction can be used. Coding conditions leading to similar effects of quantization can also be used separately or in combination with QP to determine which attribute prediction approach is to be used.

5. Pruning of Neighboring Attribute Values Used for Prediction

In some embodiments, a set of nearest reconstructed neighboring attributes of a current point is first determined for example by performing a k-d tree structure based searching process. Subsequently, the set of determined neighboring attribute values can be pruned to remove inconsistent reconstructed neighboring attribute values. The pruning process can be applied to the attribute prediction techniques disclosed herein, such as the WTA approach, weighted-sum based approach, weighted median based prediction, RD optimization based prediction, and/or the like.

A consistency check of the reconstructed neighboring attribute values can be performed in order to remove one or more inconsistent attribute values. In one example, inconsistency detection finds one or more attribute values with a lowest weight in terms of W_(a) or W_(b) compared with other neighboring attribute values. The one or more attribute values with the lowest weight can be removed from the set of reconstructed neighboring attribute values.

In an exemplary embodiment, an approximate estimate of a local gradient of the reconstructed neighboring attribute values can be considered to avoid prediction across an edge. For example, a local gradient can be estimated according to a sum of absolute attribute-value differences among the reconstructed neighboring attribute values. Alternatively, a local gradient can be estimated according to a sum of absolute attribute-value differences among a subset of the reconstructed neighboring attribute values that are along a certain direction of interest.

6. Rate-Distortion (RD) Optimization Based Selection from Multiple Prediction Techniques

In some embodiments, more than one type of attribute prediction method can be evaluated based on RD optimization performance at an encoder. Accordingly, an attribute prediction method with a highest RD optimization performance can be selected and signaled to a decoder. For example, the candidate prediction methods can include any techniques disclosed herein, such as the WTA approach, weighted-sum based approach, weighted median based prediction, RD optimization based prediction, and/or the like.

In one embodiment, a flag indicating the selected prediction method is signaled from the encoder to the decoder for prediction coding of one or a group of samples (e.g., attribute values). Based on the received flag, the decoder can determine the selected prediction method for prediction of the respective one or group of samples.

In one example, corresponding to a selected prediction method, an index indicating a predetermined subset of reconstructed attribute values can be signaled for the respective one or group of samples. Based on the received index, the decoder can determine the subset of reconstructed attribute values for prediction of the respective one or group of samples.

7. RD optimization Based Attribute Prediction

In some embodiments, an encoder or decoder can determine a group of neighboring points of a current point for attribute prediction, and associate an index with a reconstructed attribute value of each member of the group of neighboring points. The reconstructed attribute values of the group of neighboring points are used as candidates for selecting a reconstructed attribute value to be an attribute prediction of the current point. The encoder and decoder can determine the group of neighboring points and associate indices with the candidate reconstructed attribute values in an identical, or similar, way.

After the group of neighboring points is determined, at the encoder side, an RD optimization based evaluation can be performed to select a candidate attribute value from the group of neighboring samples (the reconstructed attribute values of the group of neighboring points) to be the prediction of the current point. An index corresponding to the selected neighboring sample can be signaled to the decoder side. At the decoder side, based on the received index, the same candidate determined at the encoder side, can be determined from the group of neighboring samples. The candidate can be used as the prediction of the current point at the decoder side.

(a) Forming the Group of Neighboring Points

In one embodiment, the group of neighboring points that provide candidate samples for attribute prediction of the current point is a group of nearest neighboring points of the current point in terms of geometric distances. For example, the group of nearest neighboring points can be determined by performing a k-d tree structure based search process over points of which reconstructed attribute values are already available.

The group of neighboring points that provide candidate samples can be determined with a two-step process. For example, a set of nearest neighboring points of the current point in terms of geometric distance can be determined in a first step. Thereafter, a subset of the set of nearest neighboring points can be selected to be the group of neighboring points. For example, the selection can be based on an attribute distance (e.g., median-attribute distance, or mean-attribute distance) of each member of the set of nearest neighboring points. Members with the shortest attribute distance can be determined to be the group of neighboring points. In another example, the selection can be based on an attribute distance based weight or bilateral weight (e.g., W_(a), or W_(g)) of each member of the set of nearest neighboring points. Members with the highest weights can be determined to be in the group of neighboring points. In other examples, methods different from the above may be used to determine the group of neighboring points.

(b) Index Coding Examples

FIG. 5 shows an example of assigning indices to a group (510) of candidate neighboring samples of a current point in accordance with an embodiment. As shown, the group (510) of candidate neighboring samples includes a set of samples having reconstructed attribute values 11, 43, 50, 12, 32, and 25. A sorting process is performed at the encoder side and/or decoder side to obtain a group (520) of sorted samples (521)-(526). In one example, the sorting is based on the values of each sample in the group (510). Subsequently, a set of indices are assigned to members of the group (520) with a median-first order.

For example, when the group (520) of sorted neighboring samples has an odd number of members, the member with the median value is assigned an index of 0. Then, the other members in the group (520) are assigned indices in a way that the members closer to the median value are assigned smaller indices. For a pair of members having an equal distance to the median value and located at either side of the median value, either the right-side one or the left-side one can be assigned an index first (e.g., assign a smaller index) in different embodiments.

In another example, when the group (520) of sorted neighboring samples has an even number of members, an average of the values of the two middlemost samples can be used as the median value. Then, in a similar way, the members in the group (520) are assigned indices in a way that the members closer to the median value are assigned smaller indices. For a pair of members having an equal distance to the median value and located at either side of the median value, either the right-side one or the left-side one can be assigned an index first (e.g., assign a smaller index) in different embodiments. In FIG. 5, the samples (523) and (524) are the two middle most samples. The sample (523) to the left of the respective median value can be assigned the index of 0 in one example. However, the sample (524) can be assigned the index of 0 in another example.

In an embodiment, the assigned indices in the FIG. 5 example are encoded using truncated unary code as shown in FIG. 6. The bits of the truncated unary codes can be further coded using arithmetic coding, for example, with multiple context models. In various examples, indices assigned to a group of sorted candidate neighboring samples may be coded with other types of codes other than the truncated unary code.

In an alternative embodiment, another method of coding and generating the index can be implemented to specify a neighboring sample for the WTA prediction.

When there are m (>=3) neighboring samples available for prediction, the neighboring samples may be labeled as N1, N2, . . . , Nm in the order of increasing geometric distance from the current sample. The indices of 1, 2, . . . , and m are assigned for N1, N2, . . . , and Nm, respectively, and index 0 is assigned to the weighted average prediction. Therefore, there are a total of m+1 prediction candidates.

A most probable index list (MPIL) of a predetermined size for each sample is generated based on the above-described indexing. The size of the MPIL can be, for example, 3. The index (out of 0˜m) of the best prediction chosen based upon the RD decision among the neighboring candidates is stored/included in the MPIL as the most probable index (MPI) for the sample and is coded using the truncated unary code of cMax=2. When the size of the MPIL is 3, the MPI is chosen from MPIL[0]-MPIL[2].

FIG. 7 shows a flow chart outlining an exemplary process (700) of how to generate the MPIL for each sample. In FIG. 7, MPI_Nx refers to the MPI of the neighboring sample Nx, where x can be 1, 2, 3, . . . , and m. MPI_Nx may be coded using the truncated unary code. Similar with other embodiments with truncated unary coding, each bit of the truncated unary codes may be further coded using arithmetic coding with multiple context models.

The process starts at (701) and proceeds to (S710).

At (S710), MPI_N1 is compared to MPI_N2. That is, the most probable index of N1, where N1 represents the geometrically closest neighboring sample, is compared to the most probable index of N2, where N2 represents the geometrically second closest neighboring sample. If MPI_N1=MPI_N2, then the process (700) proceeds to (S730). If MPI_N1≠MPI_N2, then the process (700) proceeds to (S720).

At (S720), when MPI_N1≠MPI_N2, that is, the most probable index of N1 is not equal to the most probable index of N2, index 0 of the MPIL for the current sample may be determined to be MPI_N1, index 1 of the MPIL for the current sample may be determined to be MPI_N2, and index 2 of the MPIL for the current sample may be determined to be 0 or the nearest remaining candidate different from MPIL[0] and MPIL[1].

At (S730), when MPI_N1=MPI_N2, that is, the most probable index of N1 is equal to the most probable index of N2, MPI_N1 is compared to 2. MPI_N1<2 means that MPI_N1 is either 0 or 1, which indicates that the prediction of the N1 sample either uses the weighted average prediction or the geometrically closest neighboring sample of N1. If MPI_N1<2, then the process (700) proceeds to (S750). If MPI_N1>2, then the process (700) proceeds to (S740).

At (S740), when MPI_N1>2, index 0 of the MPIL for the current sample can be determined to be MPI_N1, index 1 of the MPIL for the current sample can be determined to be MPI_N1-1, and index 2 of the MPIL for the current sample can be determined to be MPI_N1+1.

At (S750), when MPI_N1<2, index 0 of the MPIL for the current sample can be determined to be 0, index 1 of the MPIL for the current sample can be determined to be 1, and index 2 of the MPIL for the current sample can be determined to be 2, where 1 refers to N1, 2 refers to N2, and 3 refers to N3.

After the MPIL is generated, the index of the best prediction can be determined/chosen based on the RD decision among the neighboring candidates.

According to another embodiment, a method of coding the index is implemented to specify a neighboring sample for WTA prediction.

When there are m (>=3) neighboring samples available for prediction, the neighboring samples are labeled as N1, N2, . . . , Nm in the order of increasing geometric distance from the current sample. The indices of 1, 2, . . . , and m are assigned for N1, N2, . . . , and Nm, respectively, while index 0 is assigned to the weighted average prediction. Therefore, there are a total of m+1 prediction candidates.

A most probable index list (MPIL) of size m for each sample is generated based on the above-described indexing. The index (out of 0˜m) of the best prediction chosen based upon the RD decision among the neighboring candidates is stored in the MPIL as the most probable index (MPI) for the sample and is coded using the truncated unary code. The determinations of entries MPIL[0]-MPIL[2] follow the same process/algorithm described in FIG. 7. For MPIL[0]˜MPIL[m], the remaining m−2 candidates may be placed in the order of increasing geometric distance from the sample. For example, MPIL[3] may be determined to be the geometrically closest candidate except the candidates indicated by MPIL[0]-MPIL[2]. Index 0 may indicate weighted average candidate. When index 0 is not included in any of MPIL[0]-MPIL[2], index 0 may be placed at a designated position such as MPIL[0]. After the MPIL is generated, the index (out of 0˜m) of the best prediction can be determined/chosen based on the RD decision among the neighboring candidates.

FIG. 8 shows an example of associating indices with multiple groups (811)-(813) of candidate neighboring samples in accordance with an embodiment. For example, points of a point cloud are each associated with multiple attributes, such as attribute values of RGB color channels. In this case, a group of candidate neighboring points of a current point can be associated with the groups (811)-(813) of neighboring reconstructed samples. Each of the groups (811)-(813) corresponds to one of the RGB color channels. An encoder or decoder can first perform a sorting process to sort attribute values of each of the groups (811)-(813) according to sample values in each respective group. As a result, three groups (821)-(823) of sorted samples can be obtained as shown in FIG. 8.

Subsequently, in a way similar to the method used in the FIG. 5 example, the three groups of sorted samples can be assigned indices, for example with a median-first order. As shown, the samples in each group (821)-(823) are assigned from the left to the right with indices 4, 2, 0, 1, 3, and 5.

During operations of determining an attribute prediction for each color channel of the current point based on an RD optimization based evaluation process, the RGB color channels can be processed independently in one embodiment. As a result, three indices corresponding to the three groups (821)-(823) can be determined, and signaled to the decoder side. For example, the resultant indices can be coded with truncated unary codes or other suitable codes, and further compressed using arithmetic coding possibly with context models.

FIG. 9 shows an example of assigning indices based on costs of attribute vectors in accordance with an embodiment. For example, points of a cloud can each be associated with an attribute vector. Each attribute vector can include a set of attribute values, such as attribute values of RGB color channels. In this scenario, a group of neighboring points of a current point can be associated with a group of neighboring attribute vectors (911)-(916) including candidate reconstructed attribute values available for attribute prediction for the current point.

An encoder or decoder can first determine a cost for each attribute vector (911)-(916) based on a cost function. In one example, the cost function is defined as follows:

ƒ(X _(j))=Σ_(i=1) ^(N) ∥X _(j) −X _(i)∥₁,

where ƒ(X_(j)) represents a cost corresponding to a neighboring attribute vector represented by X_(j), X_(i) is a neighboring attribute vector with i=

and ∥.∥₁ is an L₁ norm. A vector X_(j) minimizing the cost function is defined as a vector median (X_(VM)). In other examples, depending on statistics of the attribute vectors, other cost functions can be used. For example, a different vector norm may be used for determining the costs instead of the L₁ norm.

Next, the encoder or decoder may sort the neighboring attribute vectors, for example, in an ascending order, based on the costs of the neighboring attribute vectors. Then, indices are assigned to each attribute vectors in an order consistent with the sorting order. For example, ascending indices starting from 0 are assigned corresponding to the ascending order of the neighboring attribute vectors. In FIG. 8, the attribute vectors (911)-(916) have the costs of 360, 510, 456, 414, 384, and 328, respectively. Accordingly, after the sorting operation, the attribute vectors (911)-(916) are rearranged in an order of (916), (911), (915), (914), (913), and (912), as shown in FIG. 8. Then, indices from 0 to 5 are assigned to the sorted attribute vectors from the lowest cost to the highest cost.

Finally, different from FIG. 8, the designated index of the chosen candidate vector which minimizes the RD cost is encoded with truncated unary codes or other suitable codes, and further compressed using arithmetic coding possibly with context models.

(c) Extra Conditions for Index Coding

A sampling grid of point cloud data typically is not uniform. When coding attribute values of a point cloud, the number of neighboring reconstructed samples selected for attribute prediction of a current point can vary depending on the location of such a current point in the point cloud. Accordingly, in one embodiment, instead of coding an index regardless of a parity of the number of neighboring samples of a current point as described above, the median sample value itself can be used for one chosen parity case. As a result, side-information cost of coding indices of candidate neighboring samples can be saved.

For example, the index coding (or assigning) as described above is performed for a scenario where the number of neighboring samples is even, while a median value is used for a scenario where the number of neighboring samples is odd. Alternatively and conversely, the index coding is performed for the odd number of neighboring sample scenarios while the median value is used for the even number of neighboring sample scenarios. In this way, no index is signaled when a median value is used as the attribute prediction, thus saving coding bits.

In another embodiment, an RD optimization based attribute prediction (with index coding or assigning) is invoked when a group of neighboring samples available for attribute prediction of a current point are not homogeneous according to a certain criteria. Or, in other words, the RD optimization based attribute prediction can be invoked when a variability of a group of neighboring samples available for attribute prediction of a current point is above or equal to a threshold. For example, when a maximum attribute value difference among the neighboring samples is above or equal to a certain threshold, it can be considered inhomogeneous. As another example, a local gradient of reconstructed neighboring attribute values can be used to detect an edge which renders the respective neighboring region inhomogeneous. In contrast, when the group of neighboring samples is homogeneous, a WTA type scheme or a weighted-sum or weighted-average of neighboring samples can be adopted for attribute prediction of the current point.

In another embodiment, the indexing of sorted samples described above can be performed by additionally considering a geometric distance of a candidate predictor sample from a current sample (sample of a current point). As shown in FIG. 10, a group (1010) of neighboring reconstructed samples of a current sample is sorted based on sample values resulting in a group (1020) of sorted samples (1021)-(1026). In case 1, a set of indices are assigned to the sorted samples (1021)-(1026) according to a median-first order. By considering geometric distances of the candidate samples (1021)-(1026), the index can be assigned as shown in case 2 as opposed to case 1. Specifically, the indices of the samples (1023) and (1024) are switched if the sample (1024) is geometrically closer to the current sample than the sample (923). Similarly, in case 3, when the sample (1025) is geometrically closer to the current sample than the sample (1022), the index can be assigned in a way different from case 2. Specifically, the sample (1025) is adjusted to have a smaller index value than the sample (1022).

In another embodiment, the RD optimization decision made by the encoder is used to identify the true attribute value of the current sample and an index is sent to specify a neighboring sample to be used as prediction for the current sample to be coded, as described above.

In some examples, an additional condition check can be imposed to decide whether to perform the RD decision based choice of a single neighbor sample as prediction (i.e., WTA-prediction). For example, a local variability of sample attribute values can be estimated and the RD based WTA-prediction is performed only if the variability value is higher than a certain threshold. This often leads to more efficient rate-distortion trade-off as a simple weighted average of neighboring attribute values is more effective in a smooth and monotonous region and it does not require extra signaling bits by synchronizing such threshold checking process both at the encoder and the decoder based on the reconstructed neighboring attribute values. The variability of neighboring sample attribute values can be approximated by, for example, the variance, the maximum difference, or the sum of absolute difference of attribute values among neighboring samples.

In some examples, the RD based WTA-prediction is performed only if a local gradient of attribute values indicates the edges are present in the local/neighboring region. The edges indicate that the neighboring region may be inhomogeneous. Otherwise, a simple weighted average prediction may be performed.

In some examples, different subsets, templates or locations of neighboring samples can be used for the RD decision depending on the presence, absence, or direction of edges in the local region.

In some examples, a careful design of the number of prediction candidates used for the RD decision is important because using more prediction candidates implies potentially smaller distortion at the cost of higher side-information coding bitrates. The following discussion describes using a gradual transition of the number of prediction candidates for the current sample based upon the variability of attribute values of the samples in the neighborhoods. A different number of neighboring samples can be used for the RD based WTA-prediction depending on the variability of neighboring sample attribute values.

FIG. 11 shows an example of a gradual transition of the number of neighbors for WTA-prediction. Specifically, FIG. 11 describes the use of a variable number of candidates for the RD based WTA-prediction, where, instead of using N neighbors when the attribute variability is above the WTA-threshold, a transition region is defined by two parameters a and 13 in which only M (M<N) neighbors are used as prediction candidates for the RD based WTA decision process.

When a measurement of variability of attribute values of the neighboring samples is above the β threshold, N neighboring samples are used as prediction candidates for the RD based WTA-prediction decision process. When a measurement of variability of attribute values of the neighboring samples is above the α threshold and below the β threshold, M neighboring samples are used as prediction candidates for the RD based WTA-prediction decision process. When a measurement of variability of attribute values of the neighboring samples is below the α threshold, RD based WTA-prediction is not performed for the attribute value prediction of the current sample. Instead, a weighted average prediction is performed for the attribute value prediction of the current sample.

In some examples, the β threshold is higher than the regular WTA-prediction threshold and the α threshold is below the regular WTA-prediction threshold.

This process can be generalized by introducing more transition regions in a similar manner. The advantage of this process is that it can save the neighbor-index coding costs by reducing the number of neighbor candidates for the samples and regions with low variability and vice versa.

In practice, the variability of neighboring sample attribute values discussed in the above embodiments can be approximated by, for example, the variance, the maximum difference, or the sum of absolute difference of attribute values among neighboring samples.

III. Attribute Prediction Process Examples

FIG. 12 shows a flow chart outlining an exemplary process (1200) according to an embodiment of the disclosure. The process (1200) can be used to generate an attribute prediction of a current point of a point cloud at a decoder side. In various embodiments, the process (1200) can be executed by processing circuitry, such as the processing circuitry performing functions of the attribute prediction module (450) in the encoder (400). In some embodiments, the process (1200) is implemented in software instructions, thus when the processing circuitry executes the software instructions, the processing circuitry performs the process (1100). The process starts at (S1201) and proceeds to (S1210).

At (S1210), 3D coordinates of a set of points of a point cloud can be received. For example, the 3D coordinates can be obtained from an octree decoding process, or another decoding process. In addition, the set of points can include first points of which attribute values have been reconstructed and available for attribute prediction of a current point included in the set of points.

At (S1220), a group of neighboring points of the current point can be determined from the first points. For example, the group of neighboring points can be a group of nearest neighboring points in terms of geometric distances to the current point. Alternatively, an addition process can be performed to select a subset of the group of nearest neighboring points to be the group of neighboring points. For example, the selection can be based on attribute distances, attribute based weights, and/or bilateral weights associated with each of the group of nearest neighboring. The number of group of neighboring points may be adjusted based on a measurement of variability of neighboring points. For example, the number of group of neighboring points may be reduced when a measurement of variability of neighboring points is below a threshold. Specifically, the number of neighboring points used for the attribute value prediction of the current point may be changed from N to M as shown in FIG. 11.

At (S1230), an index is associated with each of the reconstructed attribute values of the group of neighboring points of the current point. For example, the index coding methods described herein can be used. Further, reconstructed attribute values (or samples) or attribute vectors may be sorted before assigning the indices with the reconstructed attribute values.

At (S1240), an index can be received that indicates a reconstructed attribute value selected from the reconstructed attribute values of the determined neighboring points from, for example, an encoder. The reconstructed attributed value indicated by the index may be determined based on a RD decision function.

At (S1250), the reconstructed attribute value indicated by the received index can be used as an attribute prediction of the current point. The attribute prediction can subsequently be used to generate a reconstructed attribute value of the current point, for example, by combining the attribute prediction with a respective prediction residual generated from an entropy decoding process.

The process (1200) proceeds to (S1299), and terminates at (S1299).

FIG. 13 shows a flow chart outlining an exemplary process (1300) according to an embodiment of the disclosure. The process (1300) can be used to generate an attribute prediction of a current point of a point cloud at an encoder side or a decoder side. In various embodiments, the process (1300) can be executed by processing circuitry, such as the processing circuitry performing functions of the attribute prediction module (350) in the encoder (300), or the processing circuitry performing functions of the attribute prediction module (450) in the encoder (400). In some embodiments, the process (1300) is implemented in software instructions, thus when the processing circuitry executes the software instructions, the processing circuitry performs the process (1300). The process starts at (S1301) and proceeds to (S1310).

At (S1310), 3D coordinates of a set of points of a point cloud can be received. For example, the 3D coordinates can be obtained from an octree coding or decoding process. However, other coding or decoding processes can be utilized in other embodiments. In addition, the set of points can include first points of which attribute values have been reconstructed and available for attribute prediction of a current point included in the set of points.

At (S1320), a group of neighboring points of the current point can be determined from the first points based on a most probable index of a geometrically closest neighboring point of the plurality of neighboring points. For example, the group of neighboring points can be a set of nearest neighboring points in terms of geometric distances to the current point.

At (S1330), an index is associated with each of the reconstructed attribute values of the group of neighboring points of the current point. For example, the index coding methods described herein can be used. For example, reconstructed attribute values (or samples) or attribute vectors may be sorted before assigning the indices with the reconstructed attribute values.

At (S1340), a most probable index list (MPIL) of a predetermined size for the current point is generated based on a most probable index (MPI) of a geometrically closest neighboring point. For example, the MPIL of the current point can be generated based on whether the most probable index of the geometrically closest neighboring point is the same as the most probable index of a second geometrically closest neighboring point of the plurality of neighboring points. A MPIL is generated for each sample and a MPL is determined from the MPIL for each sample. The decoder may save the received MPL for every coded point. The process of generating the MPIL may be performed in view of the process described in FIG. 7.

At (S1350), a most probable index for the current point from the most probable index list is received from, for example, the encoder. The reconstructed attribute value associated with the received most probable index for the current point may be a best predication candidate among the reconstructed attribute values of the plurality of neighboring points. The reconstructed attributed value associated with the received most probable index may be determined based on a RD decision function.

At (S1360), an attribute of the current point may be predicated based on the reconstructed attribute value associated with the received most probable index. At the decoder side, the obtained attribute prediction can be used to generate a reconstructed attribute value of the current point by adding the attribute prediction to a prediction residual of the current point generated from an entropy decoding process.

The process (1300) proceeds to (S1399), and terminates at (S1399).

IV. Computer System

The techniques described above, can be implemented as computer software using computer-readable instructions and physically stored in one or more computer-readable media. For example, FIG. 14 shows a computer system (1400) suitable for implementing certain embodiments of the disclosed subject matter.

The computer software can be coded using any suitable machine code or computer language, that may be subject to assembly, compilation, linking, or like mechanisms to create code comprising instructions that can be executed directly, or through interpretation, micro-code execution, and the like, by one or more computer central processing units (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers or components thereof, including, for example, personal computers, tablet computers, servers, smartphones, gaming devices, internet of things devices, and the like.

The components shown in FIG. 14 for computer system (1400) are exemplary in nature and are not intended to suggest any limitation as to the scope of use or functionality of the computer software implementing embodiments of the present disclosure. Neither should the configuration of components be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary embodiment of a computer system (1200).

Computer system (1400) may include certain human interface input devices. Such a human interface input device may be responsive to input by one or more human users through, for example, tactile input (such as: keystrokes, swipes, data glove movements), audio input (such as: voice, clapping), visual input (such as: gestures), olfactory input (not depicted). The human interface devices can also be used to capture certain media not necessarily directly related to conscious input by a human, such as audio (such as: speech, music, ambient sound), images (such as: scanned images, photographic images obtain from a still image camera), video (such as two-dimensional video, three-dimensional video including stereoscopic video).

Input human interface devices may include one or more of (only one of each depicted): keyboard (1401), mouse (1402), trackpad (1403), touch screen (1410), data-glove (not shown), joystick (1405), microphone (1406), scanner (1407), camera (1408).

Computer system (1400) may also include certain human interface output devices. Such human interface output devices may be stimulating the senses of one or more human users through, for example, tactile output, sound, light, and smell/taste. Such human interface output devices may include tactile output devices (for example tactile feedback by the touch-screen (1410), data-glove (not shown), or joystick (1405), but there can also be tactile feedback devices that do not serve as input devices), audio output devices (such as: speakers (1409), headphones (not depicted)), visual output devices (such as screens (1410) to include CRT screens, LCD screens, plasma screens, OLED screens, each with or without touch-screen input capability, each with or without tactile feedback capability—some of which may be capable to output two dimensional visual output or more than three dimensional output through means such as stereographic output; virtual-reality glasses (not depicted), holographic displays and smoke tanks (not depicted)), and printers (not depicted).

Computer system (1400) can also include human accessible storage devices and their associated media such as optical media including CD/DVD ROM/RW (1420) with CD/DVD or the like media (1421), thumb-drive (1222), removable hard drive or solid state drive (1423), legacy magnetic media such as tape and floppy disc (not depicted), specialized ROM/ASIC/PLD based devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computer readable media” as used in connection with the presently disclosed subject matter does not encompass transmission media, carrier waves, or other transitory signals.

Computer system (1400) can also include an interface to one or more communication networks. Networks can for example be wireless, wireline, optical. Networks can further be local, wide-area, metropolitan, vehicular and industrial, real-time, delay-tolerant, and so on. Examples of networks include local area networks such as Ethernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G, LTE and the like, TV wireline or wireless wide area digital networks to include cable TV, satellite TV, and terrestrial broadcast TV, vehicular and industrial to include CANBus, and so forth. Certain networks commonly require external network interface adapters that attached to certain general purpose data ports or peripheral buses (1449) (such as, for example USB ports of the computer system (1400)); others are commonly integrated into the core of the computer system (1400) by attachment to a system bus as described below (for example Ethernet interface into a PC computer system or cellular network interface into a smartphone computer system). Using any of these networks, computer system (1400) can communicate with other entities. Such communication can be uni-directional, receive only (for example, broadcast TV), uni-directional send-only (for example CANbus to certain CANbus devices), or bi-directional, for example to other computer systems using local or wide area digital networks. Certain protocols and protocol stacks can be used on each of those networks and network interfaces as described above.

Aforementioned human interface devices, human-accessible storage devices, and network interfaces can be attached to a core (1440) of the computer system (1400).

The core (1440) can include one or more Central Processing Units (CPU) (1441), Graphics Processing Units (GPU) (1442), specialized programmable processing units in the form of Field Programmable Gate Areas (FPGA) (1443), hardware accelerators for certain tasks (1444), and so forth. These devices, along with Read-only memory (ROM) (1445), Random-access memory (1446), internal mass storage such as internal non-user accessible hard drives, SSDs, and the like (1447), may be connected through a system bus (1448). In some computer systems, the system bus (1448) can be accessible in the form of one or more physical plugs to enable extensions by additional CPUs, GPU, and the like. The peripheral devices can be attached either directly to the core's system bus (1448), or through a peripheral bus (14249). Architectures for a peripheral bus include PCI, USB, and the like.

CPUs (1441), GPUs (1442), FPGAs (1443), and accelerators (1444) can execute certain instructions that, in combination, can make up the aforementioned computer code. That computer code can be stored in ROM (1445) or RAM (1446). Transitional data can be also be stored in RAM (1446), whereas permanent data can be stored for example, in the internal mass storage (1447). Fast storage and retrieve to any of the memory devices can be enabled through the use of cache memory, that can be closely associated with one or more CPU (1441), GPU (1442), mass storage (1447), ROM (1445), RAM (1446), and the like.

The computer readable media can have computer code thereon for performing various computer-implemented operations. The media and computer code can be those specially designed and constructed for the purposes of the present disclosure, or they can be of the kind well known and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system having architecture (1400), and specifically the core (1440) can provide functionality as a result of processor(s) (including CPUs, GPUs, FPGA, accelerators, and the like) executing software embodied in one or more tangible, computer-readable media. Such computer-readable media can be media associated with user-accessible mass storage as introduced above, as well as certain storage of the core (1440) that are of non-transitory nature, such as core-internal mass storage (1447) or ROM (1445). The software implementing various embodiments of the present disclosure can be stored in such devices and executed by core (1440). A computer-readable medium can include one or more memory devices or chips, according to particular needs. The software can cause the core (1440) and specifically the processors therein (including CPU, GPU, FPGA, and the like) to execute particular processes or particular parts of particular processes described herein, including defining data structures stored in RAM (1446) and modifying such data structures according to the processes defined by the software. In addition or as an alternative, the computer system can provide functionality as a result of logic hardwired or otherwise embodied in a circuit (for example: accelerator (1444)), which can operate in place of or together with software to execute particular processes or particular parts of particular processes described herein. Reference to software can encompass logic, and vice versa, where appropriate. Reference to a computer-readable media can encompass a circuit (such as an integrated circuit (IC)) storing software for execution, a circuit embodying logic for execution, or both, where appropriate. The present disclosure encompasses any suitable combination of hardware and software.

While this disclosure has described several exemplary embodiments, there are alterations, permutations, and various substitute equivalents, which fall within the scope of the disclosure. It will thus be appreciated that those skilled in the art will be able to devise numerous systems and methods which, although not explicitly shown or described herein, embody the principles of the disclosure and are thus within the spirit and scope thereof. 

What is claimed is:
 1. A method of processing point cloud data at a decoder, comprising: receiving three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point, each of the first points being associated with a reconstructed attribute value; determining a plurality of neighboring points of the current point from the first points; associating an index with each of the reconstructed attribute values of the plurality of neighboring points; receiving a first index indicating a reconstructed attribute value selected from the reconstructed attribute values of the plurality of neighboring points, the reconstructed attributed value indicated by the first index being determined based on a rate-distortion decision function; and determining the reconstructed attribute value having the first index to be an attribute prediction of the current point.
 2. The method of claim 1, further comprising: associating the first index with each of the reconstructed attribute values of the plurality of neighboring points only when a measurement of variability of the reconstructed attribute values of the plurality of neighboring points exceeds or equals to a first threshold; otherwise, determining the attribute prediction of the current point based on a weighted average of the reconstructed attribute values of the neighboring points.
 3. The method of claim 1, further comprising: associating the index with each of the reconstructed attribute values of the plurality of neighboring points only when a local gradient of the reconstructed attribute values of the plurality of neighboring points indicates a neighboring region of the current point is inhomogeneous.
 4. The method of claim 3, further comprising: determining a subset of the plurality of neighboring points based on whether the neighboring region of the current point is inhomogeneous.
 5. The method of claim 1, further comprising: reducing a number of the plurality of neighboring points when a measurement of variability of the reconstructed attribute values of the plurality of neighboring points is below or equal to a second threshold; associating the index with each of the reconstructed attribute values of only the reduced number of the plurality of neighboring points; receiving the first index indicating a reconstructed attribute value selected from the reduced number of the reconstructed attribute values of the determined neighboring points, the reconstructed attributed value indicated by the first index being determined based on the rate-distortion function; and determining the reconstructed attribute value having the first index to be the attribute prediction of the current point.
 6. The method of claim 2, wherein the variability includes one of a variance, a maximum difference, or a sum of absolute difference of the reconstructed attribute values of the plurality of neighboring points.
 7. A method of processing point cloud data at a decoder, comprising: receiving three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point, each of the first points being associated with a reconstructed attribute value; determining a plurality of neighboring points of the current point from the first points based on a geometric distance between each of the first points and the current point; associating an index with the reconstructed attribute value of each of the plurality of neighboring points; generating a most probable index list of a predetermined size for the current point based on a most probable index of a geometrically closest neighboring point of the plurality of neighboring points; receiving a most probable index for the current point from the most probable index list, the reconstructed attribute value associated with the received most probable index for the current point being a best predication candidate among the reconstructed attribute values of the plurality of neighboring points; and predicting an attribute of the current point based on the reconstructed attribute value associated with the received most probable index.
 8. The method of claim 7, wherein the most probable index for the current point is determined based on a determination that the most probable index of the geometrically closest neighboring point is the same as the most probable index of a second geometrically closest neighboring point of the plurality of neighboring points.
 9. The method of claim 7, wherein the most probable index list for the current point includes an index indicating a weighted average predication.
 10. The method of claim 8, further comprising: associating indices 1 to M (where M is an integer larger than 1) with the plurality of neighboring candidates in a geometrically ascending order; associating indices 1 to N (where N is an integer larger than 1) with a plurality of neighboring candidates of the geometrically closest candidate in the geometrically ascending order; designating index 0 as a weighted average candidate indicating a weighted average predication; and determining the most probable index list for the current point based on a determination that the most probable index of the geometrically closest candidate is less than
 2. 11. The method of claim 7, wherein the most probable index for the current point is determined based on a rate-distortion decision function.
 12. An apparatus of processing point cloud data, comprising: processing circuitry configured to receive three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point, each of the first points being associated with a reconstructed attribute value; determine a plurality of neighboring points of the current point from the first points; associate an index with each of the reconstructed attribute values of the plurality of neighboring points; receive a first index indicating a reconstructed attribute value selected from the reconstructed attribute values of the plurality of neighboring points, the reconstructed attributed value indicated by the first index being determined based on a rate-distortion decision function; and determine the reconstructed attribute value having the first index to be an attribute prediction of the current point.
 13. The apparatus of claim 12, wherein the processing circuitry is further configured to associate the first index with each of the reconstructed attribute values of the plurality of neighboring points only when a measurement of variability of the reconstructed attribute values of the plurality of neighboring points exceeds or equals to a first threshold; otherwise, determine the attribute prediction of the current point based on a weighted average of the reconstructed attribute values of the neighboring points.
 14. The apparatus of claim 12, wherein the processing circuitry is further configured to determine a subset of the plurality of neighboring points based on whether the neighboring region of the current point is inhomogeneous.
 15. The apparatus of claim 12, wherein the processing circuitry is further configured to reduce a number of the plurality of neighboring points when a measurement of variability of the reconstructed attribute values of the plurality of neighboring points is below or equal to a second threshold; associate the index with each of the reconstructed attribute values of only the reduced number of the plurality of neighboring points; receive the first index indicating a reconstructed attribute value selected from the reduced number of the reconstructed attribute values of the determined neighboring points, the reconstructed attributed value indicated by the second index being determined based on the rate-distortion function; and determine the reconstructed attribute value having the second index to be the attribute prediction of the current point.
 16. An apparatus of processing point cloud data, comprising: processing circuitry configured to receive three dimensional (3D) coordinates of a set of points of a point cloud including first points and a current point, each of the first points being associated with a reconstructed attribute value; determine a plurality of neighboring points of the current point from the first points based on a geometric distance between each of the first points and the current point; associate an index with the reconstructed attribute value of each of the plurality of neighboring points; generate a most probable index list of a predetermined size for the current point based on a most probable index of a geometrically closest neighboring point of the plurality of neighboring points; receive a most probable index for the current point from the most probable index list, the reconstructed attribute value associated with the received most probable index for the current point being a best predication candidate among the reconstructed attribute values of the plurality of neighboring points; and predict an attribute of the current point based on the reconstructed attribute value associated with the received most probable index.
 17. The apparatus of claim 16, wherein the most probable index for the current point is determined based on a determination that the most probable index of the geometrically closest neighboring point is the same as the most probable index of a second geometrically closest neighboring point of the plurality of neighboring points.
 18. The apparatus of claim 16, wherein the most probable index list for the current point includes an index indicating a weighted average predication.
 19. The apparatus of claim 16, wherein the processing circuitry is further configured to associate indices 1 to M (where M is an integer larger than 1) with the plurality of neighboring candidates in a geometrically ascending order; associate indices 1 to N with a plurality of neighboring candidates of the geometrically closest candidate in the geometrically ascending order; designate index 0 as a weighted average candidate indicating a weighted average predication; and determine the most probable index list for the current point based on a determination that the most probable index of the geometrically closest candidate is less than
 2. 20. The apparatus of claim 16, wherein the most probable index for the current point is determined based on a rate-distortion decision function. 